To do a job like this the top course of brickwork should have been headers overhanging the brick face, and the cill formed by rendering the headers. I would take the cill off and replace the stretcher course with headers and re form the cill.
It almost looks like it could have been cast-in-place concrete, with a thin portion of it resting on the brickwork while the rest cantilevered out over the bricks. If everything showing is sound and tightly attached, I'd be strongly tempted to simply take the original chunk of sill and re-attach it, using a healthy layer of low-modulus epoxy gel. Make sure the bonding surfaces are squeaky-clean, and support the sill from below while the epoxy sets. A few dabs of matching stucco over the visible epoxy bonding lines (after roughening them up with a grinder) will make it as good as new.